Programmable current-limit on mains

Sounds like you need an AC benchtop power supply. Something like this is what you need: https://www.chromausa.com/product/low-power-programmable-ac-source-61600/

ADDITION

As a starting point (I'm not going to design the circuit right now but maybe someone else can piggy back off this idea), you can do something like this:

^{simulate this circuit – Schematic created using CircuitLab}

This will at least reduce your problem to a DC circuit that is much easier to manage with semiconductors and provide cycle-by-cycle current limit. The current-limit block is representative and shown with arbitrary components for my convenience. A proper circuit still needs to be designed.

As you describe, using an incandescent light bulb and connecting it in series with the Line conductor does limit FAULT current. However, I think you misunderstand the point of such a test. It determines if the Device Under Test has a fault before applying power. For example, say you have a WWII-era tube radio or TV. Chances are high that the old radio or TV has a line-to-neutral short circuit, and if you plug it in, BANG! It's time to change your underwear—the light bulb test for the short circuit. The light bulb's wattage does not matter; it must be rated for the correct voltage. If the light bulb lights up to full intensity, you have a short circuit, and you need to find it before applying power, or else it will ruin another pair of underwear. If the light bulb comes on dimly or dark, it is safe to apply power.

If that is what you are trying to do, you are overthinking this. Electrically, an incandescent light bulb is a very simple power resistor, and there is nothing programable about it. You can easily apply KISS (Keep It Simple Stupid) engineering techniques and achieve excellent results. All you need is a handful of power resistors configured in series and parallel to make a ballast. Twenty-five watts should be plenty. If the circuit voltage is 120 volts, you need roughly 575 Ohms of resistors with a power rating of 25 watts or more—a pair 250-Ohm, 10 watts or higher in series with 75 Ohms 5-watt or higher.

There are a couple of ways to use it since it will not light up. If it gets hot, you have a short. If It runs cool, you are safe to apply power. Or you can use a volt meter. If you see around 120 volts across the hot resistors, you have a short circuit to find. If you see a substantially lower voltage across the cool resistors, you are good to connect power.

We old-timers like to KISS. If the light is bright, have a fright.

I'm fixing my laptops power bricks. Keeping some current flowing would allow me to locate short circuits much more easily.

Every laptop power brick out there internally runs on DC. The first thing it does with AC is to rectify it to DC. So you don't need to worry about AC at all. It's just an unnecessary complication.

All you really need is a "lab" CV/CC 350V supply with 1A or 2A capacity. That's not too hard to make or buy. I have two 200V 1A supplies I connect in series for that purpose, for example.